Tuesday, January 28, 2014

Quick Start Guide to IBL Teaching

Disclaimer:  This is just a quick start guide, not a manual, and getting started in IBL is hard work. Please visit the IBL community to learn more at www.inquirybasedlearning.org

Step 1: Determine the overarching goals of the course, and use these big goals to help with decisions you have to make.  For example, when teaching Real Analysis 1, one of the big goals of the course is to understand deeply the fundamental concept of convergence. 

Step 2: Find/Adapt a sequence of problems.  Some course materials are available from www.jiblm.org.  Another option is to build your own set of problems, using a textbook as a guide for how to sequence the problems. 

Step 3: Understand your role as an instructor.  IBL instructors select the math problems, make assignments, select presenters, moderate and facilitate discussions, use group work appropriately, mentor, pose sub problems or special cases when the class is stuck, ensure all students are deeply engaged.

Step 4: Marketing what and why IBL to students and colleagues.  Marketing is used in the best sense of the word here.  Students and colleagues need expectations reset, especially if IBL is not commonly used at your institution.  Student buy-in is critical, especially at the beginning of the term.  Because teaching and learning are cultural activities, there exists a set of default, often unconscious assumptions of what math is, what teaching math is, and what students are “supposed” to do in a math class.  Based on the “distance from IBL” your students are, use the appropriate amount of regular, ongoing marketing and sign posting of tasks.

Step 5: Pick a rubric for grading presentations and homework.  Here’s one example.
            4 points = correct
            3 points = mostly correct, except for technical or clarity issues
            2 points = there exists a logical flaw
            1 points = went to the board

Allowing students to pause and return later once is a regularly practiced by IBLers.   Bonus points for productive failure are awarded by some IBL instructors.  A score equal to a 1 is rare.  Other rubrics exist. This is shared as a common choice.

Step 6: Keep a course diary with notes from class and thoughts as you prepare, grade, and reflect on your teaching.

Step 7: Use a spreadsheet with names in the rows and problem numbers across the top.  Use this spreadsheet to keep track of who has presented.   Separately, keep another spreadsheet with the names in the rows and days of the term across the top. This second sheet is used to keep track of participation, and helps you make data-driven decisions regarding who to call on and how to build groups that work effectively.

Wednesday, January 22, 2014

Destigmatizing Mistakes

Ed Burger, President of Southwestern University and mathematician, presented in Mike Starbird's session on Mathematics and Effective Thinking.  One of Ed Burger's main points is that we must raise mistakes to their proper level of dignity and value in the learning process.

Mistakes are stigmatized in mathematics.  Timed tests, answer-math curricula, questions from instructors that start with "What is the answer…?" all feed the perception that we are to do math right the first time, and any deviation from the correct path may be discouraged or labeled as wrong or inefficient.

While the quickest path might allow us to get through the material in class quicker in time, silent and lasting consequences sometimes take root.  Being reluctant to experiment and think for oneself is one of these consequences, resulting in underdeveloped problem-solving skills, reliance upon external validation of solutions, and for some students a damaging self-image in math that is exposed by the sentence, "I'm no good at word problems."

What does Ed Burger do about this?
  1. 5% of course grades are based on the quality of student failure.  In order to get an A in the class students must fail productively.
  2. Use specific activities to teach intentional mistake making as a positive strategy.  An example of this strategy is to give a problem to students to work on.  Their first task is to intentionally do the problem incorrectly and then share their mistake with a neighbor.  Often learning why a strategy is wrong leads to deeper insights, and getting used to making mistakes forms a habit of mind in the spirit of experimentation.  
  3. A related strategy is for the instructor to present an incorrect proof/solution, and then have the students discuss what insights we can learn from it.
Productive mistakes and experimentation are necessary ingredients of curiosity and creativity.  A person cannot develop dispositions to seek new ideas and create new ways of thinking without being willing to make mistakes and experiment.  Instructors can provide frequent, engaging in-class activities that dispel negative connotations of mistakes, and simultaneously elevate them to their rightful place as a necessary component in the process of learning.

Wednesday, January 8, 2014

Joint Mathematics Meetings IBL Sessions and Events

A list of IBL related talks and events are listed on the AIBL JMM 2014 page.  Follow this link IBL Sessions and Events at JMM2014   I look forward to seeing some of you in Baltimore next week!

Update:  See also the post by Math Ed Matters (Ernst + Hodge)

Friday, January 3, 2014

AIBL Special Projects Coordinators

SY,  Dana Ernst, and Angie Hodge
photo by Kirk Tuck

Dana Ernst, Angie Hodge, and I clearly have different, complementary skills.  As you can see, I don't like to talk much.  I must be a quiet, bookish type.  Dana is always riding his bike, so he can't hear what you say, and Angie would rather not see another ultra marathon advertisement, since she might sign up for it even though her schedule is full.

Dana and Angie are AIBL Special Project Coordinators.  They are working with AIBL to help disseminate IBL methods and support new IBLers, they are co-bloggers on Math Ed Matters, and they super supportive!  I am looking forward to working with them again in 2014!

Please visit our website to learn more about The Academy of Inquiry Based Learning

Wednesday, January 1, 2014

Happy New Year and Aim High!

Best wishes to all for a happy and successful 2014!  I'll share an oft used and famous quote, because I think it pertinent in our profession.
"The greater danger for most of us lies not in setting our aim too high and falling short; but in setting our aim too low, and achieving our mark." -- Michelangelo
The arc of learning is long, but bends towards the bold and hard working.